There are really plenty of variations but the main events are: Exiting the plane, leaving the secure terminal area, immigration, baggage claim and customs. The order of the last steps vary by location but it is difficult to go wrong. Signs indicate the way at each step plus doors and guard ensure that passengers do not do the wrong thing accidentally or intentionally. Once you leave an area, you cannot backtrack.
- Planes are disembarked roughly following a front-to-back order or sometimes middle to front and back simultaneously. This is getting less common but it happened to me this year in Europe. You have to make sure to leave with all your belongings.
- A path will lead you from the plane to the terminal. Sometimes you walk outside and airport people will guide you to make sure you stay safe. Most often now, the plane is connected by a movable tunnel called a jet-bridge which gets you into the terminal quickly. Another common method is to wait for a bus to drive you from the plane to the terminal. Again, airport employees are there at all times to ensure safety and that everyone follows instructions.
- From the terminal you are to follow the exit signs. Those will pass through the proper steps in sequence according to the airport you are at. Most international airports make you go through immigration first where you are to show your documents, including passport and visa if needed. There will be a number of kiosks, sometimes some are dedicated for nationals and residents, group of nationalities and the rest, so make sure to choose the appropriate one. They usually have a few questions for you to judge your intentions. Be honest and as clear as possible.
- The next step is often baggage claim, although is some places you pick up your luggage before or as you disembark from the plane. In the latter case, you will see people waiting for luggage to be taken out of the plane. This is also the case if you were required to check carry-on items or infant strollers at the gate. In most large airports though, your luggage will be delivered to a carousel as you leave the immigration area. Keep your flight number handy as large airports have a number of carousels and you have to find the right one for your flight. An electronic sign indicates which is the right one. It may also be announced by the flight crew before landing.
- There is sometimes but not always also a customs check. In some places it is optional and there will be two paths, one marked Nothing to Declare and another. If you do have nothing to declare, follow the indicated path. You may still have to show your luggage, let it be inspected and even pass it through an X-Ray machine. In some airports this is done systematically, in others it is done randomly, either based on a random light or at the discretion of custom officials. If you do have things to declare, such as when importing good which will stay in the country or bringing in commercial merchandise, you have to follow the other path where you will be asked to fill out an official form. They may demand duty on the goods or a guaranty to ensure that the good depart with you at the end of your trip.
There are indeed a few steps but they are usually easy to follow because the majority of passengers have to go through the same steps and the order is dictated by the policies of the airport at which you are arriving.
If something goes wrong, notify an official immediately before proceeding the the next area. Should your luggage not arrive, for example, you usually have to fill out a form before proceeding to customs. At customs you will have to mention this to them because you will probably return to collect your stuff once the airport contacts you when your belongings are located. In some cases, they will send them via courier but that is usually the exception.
Once you have cleared all the necessary steps, you will need to locate transport to your destination, unless someone is picking you up. In any case, I recommend two more steps before leaving the airport: Use an ATM to get local currency, Pick up complementary maps and guides to the area.
As comments mention, you will often be supplied the customs form on the plane so you you can fill it in advance, which you should as it saves time later. They will also sometimes give you a different form based on your nationality. Citizens of the arriving country or countries allied with it (EU or Andean for sample) get one form and the rest get another. When there is one form, there will usually be sections to fill out for arriving nationals and tourists, plus common ones.
Having to pass immigration and customs is not universal, sometimes they are done in a single step too. The most common reason to skip those steps though is to have done them before. This usually happens if the last leg of your journey is domestic. For example, when flying to Galapagos (Ecuador) from another country, you will usually land in Guayaquil or Quito, do immigration and customs there and then switch planes for your final leg. A few places have such traffic between countries that you do immigration on departure, this happens when travelling from Montreal (Canada) to the the USA and from Nassau (Bahamas) to the USA. Probably other places do this too but those are the ones I've seen.